A store has a $25\%$ off sale on coats. With this discount, the price of one coat is $\$34.50$. What is the original price of the coat? $\$$
Answer: The discount is $25\%$, so the discounted cost represents the original price $(100\%)$ minus the discount $(25\%)$. $100\%-25\%=75\%$ The discounted price of $\$34.50$ is $75\%$ of the original price. To find the original price, first we need to answer, $\${34.50}$ is ${75}\%$ of what number? Percent means per hundred, so ${75}\%$ is equivalent to ${\dfrac{75}{100}}$ which is also equal to ${75 \div 100}$. ${75 \div 100 = 0.75}$ To find the original price, we need to know ${0.75}$ times what number equals ${34.50}$. ${0.75} {x} = {\$34.50}$ $\begin{aligned} {0.75} {x} &= {\$34.50} \\\\ \dfrac{{0.75} {x}}{{0.75}} &= \dfrac{{\$34.50}}{{0.75}} \\\\ {x} &= {46} \end{aligned}$ The original price of the coat is $\${46}$.